The History of Categorical Logic
... is clear that categories are conceptually required for the systematic and rigorous definition of natural transformations, but at the same time, they cannot be legitimate mathematical entities unless certain precautions are taken with respect to their size. Eilenberg and Mac Lane explicitly recognize ...
... is clear that categories are conceptually required for the systematic and rigorous definition of natural transformations, but at the same time, they cannot be legitimate mathematical entities unless certain precautions are taken with respect to their size. Eilenberg and Mac Lane explicitly recognize ...
x - Loughborough University Intranet
... • Every theorem of a given deductive theory is satisfied by any model of the axiomatic system of this theory; moreover at every theorem one can associate a general logical statement logically provable that establishes that the considered theorem is satisfied in any model of this ...
... • Every theorem of a given deductive theory is satisfied by any model of the axiomatic system of this theory; moreover at every theorem one can associate a general logical statement logically provable that establishes that the considered theorem is satisfied in any model of this ...
MATH20302 Propositional Logic
... Remark: Following the usual convention in mathematics we will use symbols such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). ...
... Remark: Following the usual convention in mathematics we will use symbols such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). ...
lecture notes in logic - UCLA Department of Mathematics
... disjoint, there exists a set z which intersects each member of x in exactly one point, i.e., if y ∈ x, then there exists exactly one u such that u ∈ y and also u ∈ z. (8) Replacement: for every set x and every “definite operation” F which assigns a set F (v) to every set v, the image F [x] of x by F ...
... disjoint, there exists a set z which intersects each member of x in exactly one point, i.e., if y ∈ x, then there exists exactly one u such that u ∈ y and also u ∈ z. (8) Replacement: for every set x and every “definite operation” F which assigns a set F (v) to every set v, the image F [x] of x by F ...
Propositional Logic
... which is even more serious, is that the meaning of an English sentence can be ambiguous, subject to different interpretations depending on the context and implicit assumptions. If the object of our study is to carry out precise rigorous arguments about assertions and proofs, a precise language whose ...
... which is even more serious, is that the meaning of an English sentence can be ambiguous, subject to different interpretations depending on the context and implicit assumptions. If the object of our study is to carry out precise rigorous arguments about assertions and proofs, a precise language whose ...
Teach Yourself Logic 2017: A Study Guide
... the beginnings of mathematical logic. Or again, try one of the books I’m about to mention, skipping quickly over what you already know. L3. If you have taken an elementary logic course based on a substantial text like the ones mentioned in just a moment, then you should be well prepared. Here then, ...
... the beginnings of mathematical logic. Or again, try one of the books I’m about to mention, skipping quickly over what you already know. L3. If you have taken an elementary logic course based on a substantial text like the ones mentioned in just a moment, then you should be well prepared. Here then, ...
